How Do You Calculate the Charges on Two Repelling Particles?

In summary, two point particles with a separation of 0.4 m and a total charge of 185 µC repel each other with a force of 80 N. To find the individual charges on each particle, the formula F = k* (q1*q2)/(r^2) can be used. However, after rearranging the formula and using it in a calculator, it gives an intersect point of x = 184.9 instead of the expected result. The questions to consider are: What happened to the constant value k in the formula? And, should the micro coulombs unit be factored into the calculation as well?
  • #1
fallen186
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0

Homework Statement


Two point particles separated by 0.4 m carry a total charge of 185 µC.
(a) If the two particles repel each other with a force of 80 N, what are the charges on each of the two particles?


Homework Equations


F = k* (q1*q2)/(r^2)


The Attempt at a Solution


I tried using altering the formula so it would be 80 = (185-x)*(x) /(.4^2). I tried putting this in my calculator in which y1 = (185-x)*(x)/(.4^2), y2= 80 yet it tells me it intersects at x = 184.9. Um what did i do wrong? I would appreciate the help :).
 
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  • #2
Two quick questions: What happened to k? and Shouldn't you do something with that micro coulombs that follows the 185?
 
  • #3


As a scientist, it is important to carefully check your calculations and equations to ensure accuracy in your results. In this case, it seems that you may have made a mistake in setting up the equation for the force. The correct equation should be F = k*q1*q2/(r^2), where q1 and q2 are the charges on the two particles and r is the distance between them.

Using this corrected equation, we can rearrange to solve for the charges on the particles:

80 = (9*10^9)*(q1*q2)/(.4^2)
80 = (9*10^9)*(185-x)*x/(.4^2)
80 = (1.6875*10^11)*(185-x)*x
80 = 31218750000 - (1.6875*10^11)*x^2
(x^2) = (31218750000 - 80)/(1.6875*10^11)
x = √(31218699920/1.6875*10^11)
x = 0.00007858 or -0.00007858

Since the charges of the particles cannot be negative, we can conclude that the charges on the two particles are approximately 0.00007858 C and 184.99992142 C.

It is also important to note that these values are approximations and may vary slightly depending on the level of precision used in the calculations. As a scientist, it is important to always double check your work and use appropriate levels of precision in order to obtain accurate results.
 

Related to How Do You Calculate the Charges on Two Repelling Particles?

1. What is the "Discrete Charge problem"?

The Discrete Charge problem is a concept in physics that deals with the discrete nature of electric charge. It refers to the fact that electric charge is quantized, meaning it can only exist in discrete, specific amounts.

2. Why is the Discrete Charge problem important?

The Discrete Charge problem is important because it helps us understand the fundamental nature of electric charge and its behavior. It also allows us to accurately measure and predict the behavior of electrically charged particles.

3. How is the Discrete Charge problem related to the concept of a Coulomb?

The Discrete Charge problem is related to the concept of a Coulomb because a Coulomb is the unit of measurement for electric charge. The Discrete Charge problem explains why electric charge can only exist in specific, quantized amounts, and a Coulomb is the unit used to measure those amounts.

4. What evidence supports the existence of the Discrete Charge problem?

There is a vast amount of evidence that supports the existence of the Discrete Charge problem. One of the most convincing pieces of evidence is the Millikan oil drop experiment, which demonstrated that electric charge exists in discrete, quantized amounts. Additionally, the behavior of electrically charged particles, such as in the behavior of atoms and molecules, further supports the Discrete Charge problem.

5. Can the Discrete Charge problem be applied to other types of charges?

Yes, the Discrete Charge problem can be applied to other types of charges, such as magnetic charge (also known as "magnetic monopoles"). Just like electric charge, magnetic charge is also quantized, meaning it can only exist in discrete amounts. This follows the same principle as the Discrete Charge problem.

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